Question 1

Find the domain of $f ( x ) = \frac { x ^ { 2 } - 25 } { x ^ { 2 } + 3 x - 40 }$ .

Accepted Answer

A) all real numbers 
B) all real numbers except x = -8 
C) all real numbers except x = 5 and x = -8 
D) all real numbers except x = 8 and x = -5 
E) all real numbers except x = -5, x = 5 and x = -8 
A) all real numbers 
B) all real numbers except x = -8 
C) all real numbers except x = 5 and x = -8 
D) all real numbers except x = 8 and x = -5 
E) all real numbers except x = -5, x = 5 and x = -8

Question 2

An open box is to be made from a square piece of cardboard, 33 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).Determine the function, V, in terms of x, that represents the volume of the box.

Accepted Answer

A)  $V ( x ) = - 4 x ^ { 3 } + 66 x ^ { 2 } - 33 x$ 
B)  $V ( x ) = - 2 x ^ { 3 } + 33 x ^ { 2 }$ 
C)  $V ( x ) = 4 x ^ { 3 } - 132 x ^ { 2 } + 1089 x$ 
D)  $V ( x ) = - 4 x ^ { 3 } + 66 x ^ { 2 }$ 
E)  $V ( x ) = 4 x ^ { 3 } - 66 x ^ { 2 } + 33 x$ 
A)  $V ( x ) = - 4 x ^ { 3 } + 66 x ^ { 2 } - 33 x$ 
B)  $V ( x ) = - 2 x ^ { 3 } + 33 x ^ { 2 }$ 
C)  $V ( x ) = 4 x ^ { 3 } - 132 x ^ { 2 } + 1089 x$ 
D)  $V ( x ) = - 4 x ^ { 3 } + 66 x ^ { 2 }$ 
E)  $V ( x ) = 4 x ^ { 3 } - 66 x ^ { 2 } + 33 x$

Question 3

The function $f ( x ) = x ^ { 2 } - 5$ is one-to-one on the domain $( x \leq 0 )$ .Find $f ^ { - 1 } ( x )$ .

Accepted Answer

A)  $f ^ { - 1 } ( x ) = x ^ { 2 } + 5$ 
B)  $f ^ { - 1 } ( x ) = \sqrt { x + 5 }$ 
C)  $f ^ { - 1 } ( x ) = - \sqrt { x + 5 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { 1 } { x ^ { 2 } - 5 }$ 
E)  $f ^ { - 1 } ( x ) = \sqrt { x - 5 }$ 
A)  $f ^ { - 1 } ( x ) = x ^ { 2 } + 5$ 
B)  $f ^ { - 1 } ( x ) = \sqrt { x + 5 }$ 
C)  $f ^ { - 1 } ( x ) = - \sqrt { x + 5 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { 1 } { x ^ { 2 } - 5 }$ 
E)  $f ^ { - 1 } ( x ) = \sqrt { x - 5 }$

Question 4

Perform the addition or subtraction and write the result in standard form. 
 $19 i - ( 15 - 3 i )$

Accepted Answer

A)   $15 + 22 i$ 
B)  $- 15 - 22 i$ 
C)   $15 - 22 i$ 
D)   $- 15 + 22 i$ 
E)   $- 15 + 25 i$ 
A)   $15 + 22 i$ 
B)  $- 15 - 22 i$ 
C)   $15 - 22 i$ 
D)   $- 15 + 22 i$ 
E)   $- 15 + 25 i$

Question 5

Write the quotient in standard form. 
 $\frac { 4 + i } { 4 - i }$

Accepted Answer

A)  $\frac { 15 } { 17 }$ - $\frac { 8 } { 17 }$ i 
B)  $\frac { 15 } { 17 }$ + $\frac { 17 } { 8 }$ i 
C)  $\frac { 15 } { 17 }$ + $\frac { 8 } { 17 }$ i 
D)  $\frac { 17 } { 15 }$ + $\frac { 17 } { 8 }$ i 
E)  $\frac { 17 } { 15 }$ + $\frac { 8 } { 17 }$ i 
A)  $\frac { 15 } { 17 }$ - $\frac { 8 } { 17 }$ i 
B)  $\frac { 15 } { 17 }$ + $\frac { 17 } { 8 }$ i 
C)  $\frac { 15 } { 17 }$ + $\frac { 8 } { 17 }$ i 
D)  $\frac { 17 } { 15 }$ + $\frac { 17 } { 8 }$ i 
E)  $\frac { 17 } { 15 }$ + $\frac { 8 } { 17 }$ i

Question 6

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy the following inequality.  
Equation: $y = \frac { 7 x } { x ^ { 2 } + 6 }$  
Inequality: $y \geq 1$

Accepted Answer

A)    $1 \leq x \leq 6$ 
B)     $1 \leq x < 6$ 
C)     $1 < x < 6$ 
D)    $1 < x \leq 6$ 
E)    $1 < x \leq 6$ 
A)    $1 \leq x \leq 6$ 
B)     $1 \leq x < 6$ 
C)     $1 < x < 6$ 
D)    $1 < x \leq 6$ 
E)    $1 < x \leq 6$

Question 7

A small theater has a seating capacity of 2000.When the ticket price is $20, attendance is 1500.For each $1 decrease in price, attendance increases by 50.The revenue R of the theater as a function of ticket price x is as follows $R ( x ) = - 50 x ^ { 2 } + 2500 x , 10 \leq x \leq 20$ What ticket price will yield a maximum revenue?

Accepted Answer

A) $55.00 
B) $35.00 
C) $25.00 
D) $45.00 
E) $65.00 
A) $55.00 
B) $35.00 
C) $25.00 
D) $45.00 
E) $65.00

Question 8

The total revenue R earned (in thousands of dollars) from manufacturing handheld video games is given by   $R ( p ) = - 25 p ^ { 2 } + 1200 p$  
Where p is the price per unit (in dollars).
 
Find the revenue when the price per unit is $20.

Accepted Answer

A) $14,000,300 
B) $14,000,200 
C) $14,000,400 
D) $14,000,000 
E) $14,000,100 
A) $14,000,300 
B) $14,000,200 
C) $14,000,400 
D) $14,000,000 
E) $14,000,100

Question 9

Find a polynomial with the given zeros. 
 $i , \sqrt { 7 } , - i$

Accepted Answer

A)   $x ^ { 3 } - 7 x$ 
B)  $x ^ { 3 } - \sqrt { 7 } x ^ { 2 } + x - \sqrt { 7 }$ 
C)  $x ^ { 3 } - \sqrt { 7 } x ^ { 2 } + 7 x - \sqrt { 7 }$ 
D)  $x ^ { 3 } - 7 x ^ { 2 } + x - 7$ 
E) none of these 
A)   $x ^ { 3 } - 7 x$ 
B)  $x ^ { 3 } - \sqrt { 7 } x ^ { 2 } + x - \sqrt { 7 }$ 
C)  $x ^ { 3 } - \sqrt { 7 } x ^ { 2 } + 7 x - \sqrt { 7 }$ 
D)  $x ^ { 3 } - 7 x ^ { 2 } + x - 7$ 
E) none of these

Question 10

Use the given zero to find all the zeros of the function. ​
Function Zero
X3 + 13x2 + 59x + 87 -5 - 2i
​
​

Accepted Answer

A) 3, 5 ± 2i 
B) ±3i, -5 ± 2i 
C) -3, 5 ± 2i 
D) -3, -5 ± 2i 
E) 3, -5 ± 2i 
A) 3, 5 ± 2i 
B) ±3i, -5 ± 2i 
C) -3, 5 ± 2i 
D) -3, -5 ± 2i 
E) 3, -5 ± 2i

Question 11

Describe the error.   $\sqrt { - 8 } \sqrt { - 8 } = \sqrt { ( - 8 ) ( - 8 ) } = \sqrt { 64 } = 8$

Accepted Answer

A)   $\sqrt { - 8 } \sqrt { - 8 } = \sqrt { 8 } i \sqrt { 8 } i = 8 i = - 8 i$ 
B)   $\sqrt { - 8 } \sqrt { - 8 } = \sqrt { 8 } i \sqrt { 8 } i = - 64$ 
C)   $\sqrt { - 8 } \sqrt { - 8 } = \sqrt { 8 } i \sqrt { 8 } i = 8 i$ 
D)   $\sqrt { - 8 } \sqrt { - 8 } = \sqrt { 8 } i \sqrt { 8 } i = 8 i ^ { 2 } = - 8$ 
E)   $\sqrt { - 8 } \sqrt { - 8 } = \sqrt { 8 } i \sqrt { 8 } i = 8 i ^ { 2 } = 8$ 
A)   $\sqrt { - 8 } \sqrt { - 8 } = \sqrt { 8 } i \sqrt { 8 } i = 8 i = - 8 i$ 
B)   $\sqrt { - 8 } \sqrt { - 8 } = \sqrt { 8 } i \sqrt { 8 } i = - 64$ 
C)   $\sqrt { - 8 } \sqrt { - 8 } = \sqrt { 8 } i \sqrt { 8 } i = 8 i$ 
D)   $\sqrt { - 8 } \sqrt { - 8 } = \sqrt { 8 } i \sqrt { 8 } i = 8 i ^ { 2 } = - 8$ 
E)   $\sqrt { - 8 } \sqrt { - 8 } = \sqrt { 8 } i \sqrt { 8 } i = 8 i ^ { 2 } = 8$

Question 12

Perform the addition or subtraction and write the result in standard form.
 $( 1.5 + 6.7 i ) + ( - 7.3 + 6.5 i )$

Accepted Answer

A)   $- 5.8 + 14.2 i$ 
B)   $- 5.8 - 14.2 i$ 
C)  $- 5.8 - 13.2 i$ 
D)  $- 5.8 + 13.2 i$ 
E)  $- 5.8 + 15.2 \mathrm { i }$ 
A)   $- 5.8 + 14.2 i$ 
B)   $- 5.8 - 14.2 i$ 
C)  $- 5.8 - 13.2 i$ 
D)  $- 5.8 + 13.2 i$ 
E)  $- 5.8 + 15.2 \mathrm { i }$

Question 13

Select the correct graph of the function $f ( x ) = \frac { x - 4 } { x - 7 }$ .

Accepted Answer

A)    
B)    
C)    
D)    
E)     
A)    
B)    
C)    
D)    
E)

Question 14

The height, h(x), of a punted rugby ball is given by $h ( x ) = - \frac { 1 } { 64 } x ^ { 2 } + \frac { 21 } { 32 } x + 3$ where x is the horizontal distance in feet from the point where the ball is punted.How far, horizontally, is the ball from the kicker when it is at its highest point?

Accepted Answer

A)  $45 \text { feet }$ 
B)  $21 \text { feet }$ 
C)  $26 \text { feet }$ 
D)  $31 \text { feet }$ 
E)  $24 \text { feet }$ 
A)  $45 \text { feet }$ 
B)  $21 \text { feet }$ 
C)  $26 \text { feet }$ 
D)  $31 \text { feet }$ 
E)  $24 \text { feet }$

Question 15

Use long division to divide. $\left( x ^ { 3 } + 64 \right) \div ( x + 4 )$

Accepted Answer

A)  $x ^ { 2 } - 4 x + 16$ 
B)  $x ^ { 2 } + 4 x - 16$ 
C)  $x ^ { 2 } + 16$ 
D)  $x ^ { 2 } - 16$ 
E)  $x ^ { 2 } - 16 + \frac { 4 } { x + 4 }$ 
A)  $x ^ { 2 } - 4 x + 16$ 
B)  $x ^ { 2 } + 4 x - 16$ 
C)  $x ^ { 2 } + 16$ 
D)  $x ^ { 2 } - 16$ 
E)  $x ^ { 2 } - 16 + \frac { 4 } { x + 4 }$

Question 16

Select the graph of the function $y = ( 3 x ) ^ { 2 } - 5$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

Accepted Answer

A)     Horizontal shrink and vertical shift. 
B)     Horizontal shrink and vertical shift. 
C)     Horizontal shrink and vertical shift. 
D)     Horizontal shrink and vertical shift. 
E)    Horizontal shrink and vertical shift. 
A)     Horizontal shrink and vertical shift. 
B)     Horizontal shrink and vertical shift. 
C)     Horizontal shrink and vertical shift. 
D)     Horizontal shrink and vertical shift. 
E)    Horizontal shrink and vertical shift.

Question 17

Graph the quadratic function. ​
F (x) = x2 + 2x
​

Accepted Answer

A)    ​ 
B)    ​ 
C)    ​ 
D)    ​ 
A)    ​ 
B)    ​ 
C)    ​ 
D)    ​

Question 18

Select the graph of $y = x ^ { 4 }$ and the transformation $f ( x ) = \left( \frac { 1 } { 2 } x \right) ^ { 4 } - 2$ .

Accepted Answer

A)     
B)     
C)     
D)     
E)     
A)     
B)     
C)     
D)     
E)

Question 19

Select from the following which is the polynomial function that has the given zeros.   $1 + \sqrt { 5 } , 1 - \sqrt { 5 }$

Accepted Answer

A)  $f ( x ) = - x ^ { 2 } - 2 x - 4$ 
B)  $f ( x ) = - x ^ { 2 } - 2 x + 4$ 
C)  $f ( x ) = x ^ { 2 } - 2 x - 4$ 
D)  $f ( x ) = x ^ { 2 } - 2 x + 4$ 
E)  $f ( x ) = x ^ { 2 } + 2 x - 4$ 
A)  $f ( x ) = - x ^ { 2 } - 2 x - 4$ 
B)  $f ( x ) = - x ^ { 2 } - 2 x + 4$ 
C)  $f ( x ) = x ^ { 2 } - 2 x - 4$ 
D)  $f ( x ) = x ^ { 2 } - 2 x + 4$ 
E)  $f ( x ) = x ^ { 2 } + 2 x - 4$

Question 20

Determine the domain of the function $f ( x ) = \frac { 5 } { ( x - 2 ) ^ { 4 } }$ .

Accepted Answer

A) Domain: all real numbers except x = -5 and -2 
B) Domain: all real numbers 
C) Domain: all real numbers except x = -5 and 2 
D) Domain: all real numbers except x = 2 
E) Domain: all real numbers except x = 5 and 2 
A) Domain: all real numbers except x = -5 and -2 
B) Domain: all real numbers 
C) Domain: all real numbers except x = -5 and 2 
D) Domain: all real numbers except x = 2 
E) Domain: all real numbers except x = 5 and 2

Find the domain of $f ( x ) = \frac { x ^ { 2 } - 25 } { x ^ { 2 } + 3 x - 40 }$ .

An open box is to be made from a square piece of cardboard, 33 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).Determine the function, V, in terms of x, that represents the volume of the box.

The function $f ( x ) = x ^ { 2 } - 5$ is one-to-one on the domain $( x \leq 0 )$ .Find $f ^ { - 1 } ( x )$ .

Perform the addition or subtraction and write the result in standard form. $19 i - ( 15 - 3 i )$

Write the quotient in standard form. $\frac { 4 + i } { 4 - i }$

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy the following inequality. Equation: $y = \frac { 7 x } { x ^ { 2 } + 6 }$ Inequality: $y \geq 1$

The total revenue R earned (in thousands of dollars) from manufacturing handheld video games is given by $R ( p ) = - 25 p ^ { 2 } + 1200 p$ Where p is the price per unit (in dollars). Find the revenue when the price per unit is $20.

Find a polynomial with the given zeros. $i , \sqrt { 7 } , - i$

Use the given zero to find all the zeros of the function. Function Zero X³ + 13x² + 59x + 87 -5 - 2i

Describe the error. $\sqrt { - 8 } \sqrt { - 8 } = \sqrt { ( - 8 ) ( - 8 ) } = \sqrt { 64 } = 8$

Perform the addition or subtraction and write the result in standard form. $( 1.5 + 6.7 i ) + ( - 7.3 + 6.5 i )$

Select the correct graph of the function $f ( x ) = \frac { x - 4 } { x - 7 }$ .

The height, h(x), of a punted rugby ball is given by $h ( x ) = - \frac { 1 } { 64 } x ^ { 2 } + \frac { 21 } { 32 } x + 3$ where x is the horizontal distance in feet from the point where the ball is punted.How far, horizontally, is the ball from the kicker when it is at its highest point?

Use long division to divide. $\left( x ^ { 3 } + 64 \right) \div ( x + 4 )$

Select the graph of the function $y = ( 3 x ) ^ { 2 } - 5$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

Graph the quadratic function. F (x) = x² + 2x

Select the graph of $y = x ^ { 4 }$ and the transformation $f ( x ) = \left( \frac { 1 } { 2 } x \right) ^ { 4 } - 2$ .

Select from the following which is the polynomial function that has the given zeros. $1 + \sqrt { 5 } , 1 - \sqrt { 5 }$

Determine the domain of the function $f ( x ) = \frac { 5 } { ( x - 2 ) ^ { 4 } }$ .

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 2: Polynomial and Rational Functions

Find the domain of f(x)=x2−25x2+3x−40f ( x ) = \frac { x ^ { 2 } - 25 } { x ^ { 2 } + 3 x - 40 }f(x)=x2+3x−40x2−25​ .

An open box is to be made from a square piece of cardboard, 33 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).Determine the function, V, in terms of x, that represents the volume of the box.

The function f(x)=x2−5f ( x ) = x ^ { 2 } - 5f(x)=x2−5 is one-to-one on the domain (x≤0)( x \leq 0 )(x≤0) .Find f−1(x)f ^ { - 1 } ( x )f−1(x) .

Perform the addition or subtraction and write the result in standard form. 19i−(15−3i)19 i - ( 15 - 3 i )19i−(15−3i)

Write the quotient in standard form. 4+i4−i\frac { 4 + i } { 4 - i }4−i4+i​

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy the following inequality. Equation: y=7xx2+6y = \frac { 7 x } { x ^ { 2 } + 6 }y=x2+67x​ Inequality: y≥1y \geq 1y≥1

The total revenue R earned (in thousands of dollars) from manufacturing handheld video games is given by R(p)=−25p2+1200pR ( p ) = - 25 p ^ { 2 } + 1200 pR(p)=−25p2+1200p Where p is the price per unit (in dollars). Find the revenue when the price per unit is $20.

Find a polynomial with the given zeros. i,7,−ii , \sqrt { 7 } , - ii,7​,−i

Use the given zero to find all the zeros of the function. ​ Function Zero X3 + 13x2 + 59x + 87 -5 - 2i ​ ​

Describe the error. −8−8=(−8)(−8)=64=8\sqrt { - 8 } \sqrt { - 8 } = \sqrt { ( - 8 ) ( - 8 ) } = \sqrt { 64 } = 8−8​−8​=(−8)(−8)​=64​=8

Perform the addition or subtraction and write the result in standard form. (1.5+6.7i)+(−7.3+6.5i)( 1.5 + 6.7 i ) + ( - 7.3 + 6.5 i )(1.5+6.7i)+(−7.3+6.5i)

Select the correct graph of the function f(x)=x−4x−7f ( x ) = \frac { x - 4 } { x - 7 }f(x)=x−7x−4​ .

Use long division to divide. (x3+64)÷(x+4)\left( x ^ { 3 } + 64 \right) \div ( x + 4 )(x3+64)÷(x+4)

Select the graph of the function y=(3x)2−5y = ( 3 x ) ^ { 2 } - 5y=(3x)2−5 .Compare the graph of this function with the graph of y=x2y = x ^ { 2 }y=x2 .

Graph the quadratic function. ​ F (x) = x2 + 2x ​

Select the graph of y=x4y = x ^ { 4 }y=x4 and the transformation f(x)=(12x)4−2f ( x ) = \left( \frac { 1 } { 2 } x \right) ^ { 4 } - 2f(x)=(21​x)4−2 .

Select from the following which is the polynomial function that has the given zeros. 1+5,1−51 + \sqrt { 5 } , 1 - \sqrt { 5 }1+5​,1−5​

Determine the domain of the function f(x)=5(x−2)4f ( x ) = \frac { 5 } { ( x - 2 ) ^ { 4 } }f(x)=(x−2)45​ .

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Find the domain of $f ( x ) = \frac { x ^ { 2 } - 25 } { x ^ { 2 } + 3 x - 40 }$ .

The function $f ( x ) = x ^ { 2 } - 5$ is one-to-one on the domain $( x \leq 0 )$ .Find $f ^ { - 1 } ( x )$ .

Perform the addition or subtraction and write the result in standard form. $19 i - ( 15 - 3 i )$

Write the quotient in standard form. $\frac { 4 + i } { 4 - i }$

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy the following inequality. Equation: $y = \frac { 7 x } { x ^ { 2 } + 6 }$ Inequality: $y \geq 1$

The total revenue R earned (in thousands of dollars) from manufacturing handheld video games is given by $R ( p ) = - 25 p ^ { 2 } + 1200 p$ Where p is the price per unit (in dollars). Find the revenue when the price per unit is $20.

Find a polynomial with the given zeros. $i , \sqrt { 7 } , - i$

Use the given zero to find all the zeros of the function. Function Zero X³ + 13x² + 59x + 87 -5 - 2i

Describe the error. $\sqrt { - 8 } \sqrt { - 8 } = \sqrt { ( - 8 ) ( - 8 ) } = \sqrt { 64 } = 8$

Perform the addition or subtraction and write the result in standard form. $( 1.5 + 6.7 i ) + ( - 7.3 + 6.5 i )$

Select the correct graph of the function $f ( x ) = \frac { x - 4 } { x - 7 }$ .

Use long division to divide. $\left( x ^ { 3 } + 64 \right) \div ( x + 4 )$

Select the graph of the function $y = ( 3 x ) ^ { 2 } - 5$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

Graph the quadratic function. F (x) = x² + 2x

Select the graph of $y = x ^ { 4 }$ and the transformation $f ( x ) = \left( \frac { 1 } { 2 } x \right) ^ { 4 } - 2$ .

Select from the following which is the polynomial function that has the given zeros. $1 + \sqrt { 5 } , 1 - \sqrt { 5 }$

Determine the domain of the function $f ( x ) = \frac { 5 } { ( x - 2 ) ^ { 4 } }$ .